express the following ratios in their simplest form 4 whole 1/2:2 whole 1/4
Answers
Selina solutions
Grade 6
Biology
Mathematics
Physics
Chapters in CONCISE Mathematics - Middle School - 6
Exercises in Ratio
Question 1
Q1) Express each of the following ratios in its simplest form :
(a) (i) 4 : 6
(ii) 48 : 54
(iii) 200 : 250
(b) (i) 5 kg : 800 gm
(ii) 30 cm : 2 m
(iii) 3 m : 90 cm
(iv) 2 years : 9 months
(v) 1 hour : 45 minutes
(vi) 4 min : 45 sec
(c) \left(i\right)\ 1\frac{1}{2}:2\frac{1}{2}\ \ \ \left(ii\right)\ 3\frac{1}{2}:7\ \ \ \ \ \left(iii\right)\ 2\frac{1}{3}:3\frac{1}{2}:1\frac{1}{4}\ \ \ \left(iv\right)\ x^2:4x\ \ \ \ \left(v\right)\ 2.5:1.5\ \ \ \ \left(vi\right)\ 2.5:5(i) 1
2
1
:2
2
1
(ii) 3
2
1
:7 (iii) 2
3
1
:3
2
1
:1
4
1
(iv) x
2
:4x (v) 2.5:1.5 (vi) 2.5:5
Solution:
(a) (i)4:6=\frac{4}{6}=\frac{2}{3}=2:3(i)4:6=
6
4
=
3
2
=2:3
(ii)48:54=\frac{48}{54}=\frac{8}{9}=8:9(ii)48:54=
54
48
=
9
8
=8:9
(iii)200:250=\frac{200}{250}=\frac{4}{5}=4:5(iii)200:250=
250
200
=
5
4
=4:5
(b) (i) 5kg:800gm = 5000:800
(5 x 1000gm = 5000gm)
=\frac{5000}{800}=\frac{50}{8}=25:4=
800
5000
=
8
50
=25:4
(ii) 30cm : 2m = 30 cm : 200 cm
(3 x 100 cm = 300 cm)
=\frac{30}{200}=\frac{3}{20}=3:20=
200
30
=
20
3
=3:20
(iii) 3 m : 90 cm = 300 cm : 90 cm
( 3 x 100cm = 300 cm)
=\frac{300}{90}=\frac{10}{3}=10:3=
90
300
=
3
10
=10:3
(iv) 2 years : 9 months = 24 months : 9 months
(2 years = 2 x 12 = 24 months)
=\frac{24}{9}=\frac{8}{3}=8:3=
9
24
=
3
8
=8:3
(v) 1 hour : 45 minutes = 60 minutes : 45 minutes
( 1 hour = 60 minutes)
\frac{60}{45}=\frac{4}{3}=4:3
45
60
=
3
4
=4:3
(vi) 4 min : 45 sec = 240 sec : 45 sec
(1 minutes = 60 sec , 4 x 60 = 240 sec)
=\frac{240}{45}=\frac{16}{3}=16:3=
45
240
=
3
16
=16:3
(c)\ (i)\ 1\frac{1}{2}:2\frac{1}{2}=\frac{3}{2}:\frac{5}{2}=\frac{3}{2}\div\frac{5}{2}(c) (i) 1
2
1
:2
2
1
=
2
3
:
2
5
=
2
3
÷
2
5
=\frac{3}{2}\times\frac{2}{5}=\frac{3}{5}=3:5=
2
3
×
5
2
=
5
3
=3:5
(ii)\ 3\frac{1}{2}:7=\frac{7}{2}:\frac{7}{1}=\frac{7}{2}\div\frac{7}{1}(ii) 3
2
1
:7=
2
7
:
1
7
=
2
7
÷
1
7
=\frac{7}{2}\times\frac{1}{7}=\frac{1}{2}=1:2=
2
7
×
7
1
=
2
1
=1:2
(iii)\ 2\frac{1}{3}:3\frac{1}{2}:1\frac{1}{4}=\frac{7}{3}:\frac{7}{2}:\frac{5}{4}(iii) 2
3
1
:3
2
1
:1
4
1
=
3
7
:
2
7
:
4
5
=\frac{7}{3}\times12:\frac{7}{2}\times12::\frac{5}{4}\times12=
3
7
×12:
2
7
×12::
4
5
×12
(L.C.M of 2,3 and 4 = 12)
= 28 : 42 : 15
(iv)x^2:4x=\frac{x^2}{4x}=\frac{x\times x}{4\times x}=\frac{x}{4}=x:4(iv)x
2
:4x=
4x
x
2
=
4×x
x×x
=
4
x
=x:4
(v)\ 2.5:1.5=\frac{25}{15}=\frac{5}{3}=5:3(v) 2.5:1.5=
15
25
=
3
5
=5:3
OR,2.5:1.5=\frac{25}{10}:\frac{15}{10}=\frac{25}{10}\div\frac{15}{10}OR,2.5:1.5=
10
25
:
10
15
=
10
25
÷
10
15
=\frac{25}{10}\times\frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5:3=
10
25
×
15
10
=
15
25
=
3
5
=5:3
(vi)\ 2.5:5=\frac{25}{10}:\frac{15}{10}=\frac{25}{10}\div\frac{15}{10}(vi) 2.5:5=
10
25
:
10
15
=
10
25
÷
10
15
=\frac{25}{10}\times\frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5:3=
10
25
×
15
10
=
15
25
=
3
5
=5:3
(vi)\ 2.5:5=\frac{25}{10}:\frac{5}{1}=\frac{25}{10}\div\frac{5}{1}=\frac{25}{10}\times\frac{1}{5}(vi) 2.5:5=
10
25
:
1
5
=
10
25
÷
1
5
=
10
25
×
5
1
=\frac{5}{10}=1:2=
10
5
=1:2
OR, 2.5 : 5 = 2.5 : 5.0 = \frac{2.5}{5.0}=\frac{25}{50}=\frac{1}{2}=1:2
5.0
2.5
=
50
25
=
2
1
=1:2
Step-by-step explanation:
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